基于ANSOFT有限元仿真的变耦合系数型时栅结构优化设计

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Mar.2013机 床 与 液 压Hydromechatronics Engineering Vo1.41 No.6DOI：10.3969/j.isn.1001-3881.2013.06.012Structure Optimization Design of Time-Grating withVariable Coupling Coefi cient Based on ANSOFTElectromagnetic AnalysisJIANG Yanyun ，SHI Jinghui ，HE Jian h，TANG Qifu h，YU Lei. a.Enginering Research Center of Mechanical Detection Technology&Equipment，Ministry of Education；b.Remote Test and Control Institute，Chongqing Univeniof Technology，Chongqing 400054，China；2.Changzhou Entry-exit Inspection and Quarantine Bureau of P.R.C，Changzhou 213003，China1.IntroductionAbstract：In order to improve the signal strength of the time-grating with variable coupling coefi-cient，the air gap width between the stator and rotor(A)，the stator tooth width(B)，the toothwidth ratio of rotor and stator(C)and the tooth thickness(D)were selected as the control fac-tors.By using of an L16(4 )ohogonal array，the 1 6 diferent parametersinduction signalstrength were colected.The range analysis and the variance analysis were performed through e-lectromagnetic analysis data.The result indicates that the optimal combination found of A～D is0.300 mm，1.500 mm。4：1 and 3.000 mm ，and the induction signal increases of 16.1% .Theimpact order of the parameters for the induction signal is A>C>B>D.and A and C have a high sig-nifcant effect on the induction signa1.The method is more practical valne of construction work。

Key words：Time-Grating，ANSOFT simulation，range analysis，optimization designTime-Grating with Variable Coupling Coeficient[1]，which based on the electromagnetic inductionprinciple，takes the space of the rotor displacementconversion for induction electric signals. This typesensor has the advantages such as simple structure，low cost and high precision.Studies have shown thatstructure of the sensor will affect the induction signalintensity，and the signal is too weak will reduce sen·sor measurement stability.Finite element simulationapplication has made remarkable effect in engineeringdesign field.However，it is very difficult to get anycombination of structural parameters of the pendu-lOHS.and it takes a lot of time for modeling and coin。

Received：2012-12-09National Natural Science Foundation of China(50575235)JIANG Yanyun.E-mail：516311588### qq.conputing solution. In this paper，the orthogonal tablewas used to design the sensor structure of the differ-ent parameters combination，the finite element simu-lation was used to get the value of induction signal，and the best group of structure parameters whichmakes the induction signal be highest was obtainedthrough range analysis.Finally，through variance a·nalysis，the significant influence level of the mainstructural parameters on induction signal was accu-rately drawn，thus guiding the signal optimization de-sign of the structure。

2.Analysis the wave of time-grating sensorwith variable coupling coeficientThe key of time-Grating with Variable CouplingCoefficient is based on three-phase machinery。

The mathematical model is：咖(A)咖A·COS(ogt)COS(2，rx/W) (1)( ) Acos(wt2r/3)cos(21rx/W2 3)(2)JIANG Yanyun，et al：Structure Optimization Design of Time-Grating with VariableCoupling Coeficient Based on ANSOFT Electromagnetic垒 ! --(b(C)： Acos(t4"n/3)cos(2rx/W41T/3)(3)(ABc) 3 c。s(∞f-2rx/W) (4)Expression(4)can also write like this：UAsin(tot2百 )：Asin(tot△咖)(5)w Here，A is the signal amplitude，to is the angular fre·quency，W is the spatial of windings，A4，is the addi-tional phase angle.The time-grating enwinds the pro-pel coil and inductive coil(probe)on the tooth ofthe stator，magnetic field molds loop circuit throughthe stator，the rotor tooth and the air gap between theintertrochanteric.When the rotor rotates，the shape0f air gap between the intertroehanteric varies。thenthe magnetic resistance in the loop circuit also va-ties.Therefore，the magnetic flux of the inductoriumchanges and molds a whirled magnetic field which israpidly moved.Eventualy，it reflects in the inducedelectric motive fc，ree of the inductoriums。

3.Orthogonal design of time·gratingwith Variable coupling coeficientture parametersSenSOrstruc-The orthogonal design is the most important design method of the multi-factor experiment.It is de-signed according to the fractional principle of factordesign.Orthogonal experiment design is based on or-thogonal design of certain rules，which is to ensurethat all information of the affecting test perform anceparameters can be obtained by using a minimumnumber of tests in al-factor experiment. It can re-duce the number of finite element simulation，andensure that the sensing signals analysis and optimiza-tion is completed in minimum test number of structur-al parameters by using the orthogonal experimentaldesign to arrange sensing signals structure parameters[2]。

Fig.1 The model of Time-Grating sensorwith variable couplingInduction signals strength，which is affected bycoupling intensity between excitation coil and sensecoil，mainly relates to the magn etic circuit model andthe air magnetic lea。

Based on the four factors of the air gap width betweenthe stator and rotor(A)，the stator tooth width(B)，the tooth width ratio of rotor and stator(C)and thetooth thickness(D)，the orthogonal test，accordingto the design principle，is designed with four levelsand four factors by adopting orthogonal table L16(4 ).Using the modal analysis of large-scale finiteelement analysis software ANSO n 1 to get the value(厂)of the induction signal，the orthogonal table isnbtained as shown in Tab.1。

Tab.1 Factors assignment to orthogonal arrayof Time-grating sensor4.Induction signal range analysis of theTime-Grating sensor structure4.1.The principle of range analysisIt can solve the under two problems that usingHydromechatronics Engineeringthe range analysis method to calculate R values ineach column of the orthogonal table：1、Solving the best horizontal combination.Thisprublem comes down to find out that，which factorsare taken.the results will be better。

Calculating formula is as follows：f (6) - i (7)Among them，i is the number of levels，J is the col-umn numbers of orthogonal table，r is the number ofduplicate test ifl the same level of the factor，K is thetest average of column J and level i， is the sum ofexperimental result Y.of the column J and 1evel i inorthogonal table，and Rjis the range of the column 。

4.2.Results of range analysisAccording to the principle of range analysis，theI.esults are obtained and shown in Tab.2。

Tab.2 Results of range analysis on the inductionsignal of Time-Grating structureAs Tab.2 shown，the range size order of the fivefactors is：RA>Rc>RB>RD.That affect order oftheindication signal strength is the air gap width betweenthe stator and rotor(A)，tooth width ratio of Rotorand stator(C)，stator tooth width(B)，and thetooth thickness(D).From Fig.2 the optimal anti-vi-bration structure parameters combination， namelyA2B2C4D3，is identifed，and the width of air gapwidth between the stator and rotor is 0.300 mm，thestator tooth width is 1.500 mm.the tooth width ratioof rotor and stator is 4：1.and the tooth thickness is3.000 mm.Using the finite element model parametercombination reconstructs model and verifies the simu-lation results(Fig.3)，the induction signal strengthis signifcantly increased after optimizing.Before op-timization signal strength is 0.647 V，and the opti-mized one is 0.751 V.increased by 16.1% .Theauthors come to the conclusion that the finite elementanalysis results are coincide with the simulation re·sults，that is，the signal strength greatly improved。

0.59O.57O.55O.530.5l0.490.470.45LevelsFig.2 Influence of factors on the fundamental frequencyof Rigid-Flex backplane500.00400 OO300.O0200.00100 0O0 O0. 100.O0-200.00. 300.O040O.00. 500.0060o.0O4O0O020o.o00.0O.200.0O-4OO0O-6 O0t/mslJ 1f I.f 雌I ]l-0 O0 10.O0 2O.O0 30.O0 40.O0 50.O0t/msFig.3 Compare the signal amplitude betweenbefore and after optimizationThe size of the ranges can evaluation the size or。

der for parameters effect indication signal strength，but in order to study whether the parametersinflu-ence on the test result is signifcant，it is needed touse the variance analysis method of orthogonal vari-ance to get signifcant comparison of variance factors。

According to the remarkable results， time-gratingstructure parameters design can be targeted done，and improve its signal amplitude。

； 时 lI III-o 0JIANG Yanyun，et al：Structure Optimization Design of Time-Grating with VariableCoupling Coefficient Based on ANSOFT Electromagnetic Analysis 675.Induction signal variance analysis of thetime-grating structure5.1.The principle of variance analysis with or-thogonai experiment[3-4]The variance analysis as a way to solve the basicproblem is that by analyzing test data to study the fac。

tors that influencing the outcome of the trial is signifi。

cant.The main calculating formula is as follows：The estimate of variance S can be obtained bythe square of deviance Q divided by the corespond-ing freedomf/as folows：s 2 QE 2 ，Q 2，S 箸Defined statistic(F )：F - 里i - 2(8)(9)If.01( )>F ≥F0.05( )，i is the sig-nificant factor. If F ≥ F0. 01( )，i is the highlysignifcant factor，while if F

5.2.Variance analysis of time-grating structuralparameters[5]By multivariate statistical analysis according tothe above principle，the results table of time-gratingstructure parameter analysis is obtained(Tab.3)。

It shows that the air gap width between the statorand rotor(A)，whosefvalue reaches 2.064，is themost influential factor of indication signal strength a-mong the four structural parameters.Thus during thedesign process，the key parameter could be prioritycontroled to improve the signal amplitude.The f val-ue of each parameter by large to small is signifcantlyordered to be FA>Fc>FB>Fo.This analysis resultcoincides with the range analysis。

Tab.3 Results of variance analysis on structure parameters of Time-grating sensor6.ConclusionsBased on the electromagnetic analysis.combin-ning the application of multivariate statistical analysisto study indication signal of Time-Grating with Varia。

ble Coupling Coeficient with orthogonal experiment，the folowing conclusions can be drawn：1)It is easy for designers to intuitively observetime-grating sensor internal magnetic field distributionand get any combination of structural parameters ofthe pendulous through the electromagnetic analysis。

2)Based on range analysis of the indication sig-nal values at 1 6 species of parameters combination。

the order of the influence level on the signal strengthis obtained as A，C，and then B，D.The optimal an-ti-vibration structure parameters combination isA2B2 C4D3.It means the width of air gap width be-tween the stator and rotor is 0.300 mm.the statortooth width is 1.500 mm.the tooth width ratio of ro-tor and stator is 4：1，and the tooth thickness is3.000 mm. Before optimization signal strength is0.647 V，and the optimized one is 0.751 V，in-creased by 16.1% 。

3)By the variance analysis with orthogonal ex-periment，it is shown that the signifcant sequence offive parameters which influence the fundamental fe。

quency is FA>Fc>F口>FD.This analysis result so-incides with the range analysis.The air gap width be-tween the stator and rotor(A).the tooth width ratioof rotor and stator(C)，are less influential thanthem.However，the stator tooth widths(B)and thetooth thickness(D)，arent the signifcantly influen-tiafactnr。

Hydromechatronics EngineeringIt could greatly short the testing cycles，reducethe design cost and significantly improve the productreliability，with the combining application of the fi-nite element simulation，orthogonal experiment meth。

od and the multivariate statistical analysis method inengineering design，optimization and analysis.Thismethod is not only suitable for other engineeringfields，but also has large practical engineering value。

References：[1] YANG Wei，PENG Donglin，ZHU Ge.Design of timegrating senor based on variable coupling coefficient trans-former[J].Chinese Journal of Scientifc Instrument，2006，27(11)；1403-1405。

[2] Law R C，Raymond Cheang，Tan Y W.Thermal perform-ance prediction of QFN packages using artifcial neuralnetwork(ANN)[Z].International Electronic Manufac。

[3] Tsai M J.Optimal laser-cutting pametem for QFN pack-ages by utilizing artificial neural networks and genetic al-gorithm[J].Journal of Materials Processing Technology，2008(1/2/3)：1-14。

[4] Nelson R A.Geologic analysis of naturally fractured res。

ervoir[M].Boston：Gulf Professional Publishing House，2001：40-78。

[5] WU Zhaohua，HUANG Chunyue，ZHOU Dejian，Study onsolder joint reliability of ceramic ball grid array compo-nent based on design of experiment method[J].ChinaWelding，2006(3)：68-73。

基于 ANSOFT有限元仿真的变耦合系数型时栅结构优化设计蒋艳云h ，史经辉 ，何 健h，汤其富h，余 磊1.重庆理工大学 a.机械检测技术与装备教育部工程研究中心；b.远程测试与控制技术研究所 ，重庆 400054；2.常州出人境检验检疫局，江苏 常州 213003摘要 ：为了提高变耦合系数型时栅感应信号的强度，选取其转齿和定齿间气隙宽度(A)，定子齿宽(B)，转子与定子齿宽比(c)和齿厚度(D)4个参数，采用水平正交表L (4 )采集16种不同参数组合的感应信号强度，对电磁仿真求解结果进行极差分析和方差分析♂果表明：最优结构参数组合A-D分别为0.300 mm、1.500 mm、4：1、3.000 mm，优化后感应信号强度提高 16.1%；各参数影响信号顺序为： >C>B>D ，且 A、c显著影响信号.该方法具有较强的工程实用价值。

关键词：时栅 ；ANSOFT仿真；极差分析；优化设计中图分类号：TH86